Rolling is a metal forming process in which stock sheets or strips are passed through a pair of rolls to reduce the thickness of the stock sheets or strips. Due to the high temperatures generated from the friction of rolling, from material deformation, and/or from contacting hot incoming material, the rolls may experience thermal expansion (also referred to as thermal crown). Thermal expansion along the roll axis is referred to as the thermal crown and the average in thermal expansion along the roll axis is referred to as the thermal expansion. Accurate measurements of the thermal expansion/crown of the roll when the roll is hot are needed for many reasons, one of which is to ensure that proper adjustments are made when needed to position the rolls properly relative to the strips to ensure that the rolled metal strips are of the desired flatness and profile.
Because of the high roll temperatures and the environment of a mill, however, it is difficult to measure the profile/camber of the rolls at the required time during the rolling process. Numerical models are therefore used to simulate the evolution of the thermal expansion and thermal crown of the roll by estimating the initial conditions and the heat transfer at the roll surface. Although these numerical models do not require direct measurements, the results are limited in accuracy because of the difficulty of accurately estimating the model parameters. In some cases, thermal crown is inferred using flatness or profile measurements of the strip as it exits the roll bite, but such methods are of limited accuracy and are only useful if the entry profile of the sheet is known accurately, the mill is a single stand mill, and the mill is running. These methods also only apply to the portion of the roll in contact with the strip, and so the thermal crown of the roll located outside the strip must be estimated. In a similar way, the thermal expansion can be inferred using the measured exit strip thickness, but limitations similar to those associated with the inferred crown method also exist.
Other attempts at measuring the thermal crown of a roll involve measuring the distance between a sensor and a roll, which also has limitations. For instance, the beam upon which such sensors are mounted may deform, rendering the sensors inaccurate. Efforts to minimize beam deformation or compensate for beam deformation can be cumbersome (e.g., occupy a significant amount of space on/near the machinery) and expensive.